I think for Indian recipes you should in general look for an unstrained, set yoghurt. There are other factors that determine the final taste and texture of the yoghurt (the bacteria, the type of milk, length of fermentation, …) but you may not have much choice w.r.t. other factors than these two:
Production process: Set yoghurt is yoghurt that's made the traditional way, it's fermented in the pot that it's sold in. Stirred yoghurt on the other hand is fermented before being packaged; it's a more industrialized production process which is cheaper, but results in a more sour, thinner yoghurt. Stirred yoghurt has a smooth, pourable consistency; whereas set yoghurt is firmer. I got a bit confused when I was using stirred yoghurt the first time I tried making raita and the recipe told me to whisk the yoghurt till it was smooth. The pretty sour taste of the yoghurt also didn't go well with the spices, and the juice from the cucumbers made the already-thin yoghurt too watery. You could try fixing both problems by straining the yoghurt a bit and adding sugar, but it's better and easier to just buy set yoghurt. The yoghurt's packaging might say explicitly what type of yoghurt it is, but if it doesn't or you don't understand the language: avoid yoghurt that comes in “milk carton”-like containers, that most definitely means it's stirred yoghurt. A plastic pot doesn't mean it's set yoghurt though, but it's a better bet.
Thickness: Strained yoghurt (like “Greek-style yoghurt” in Europe and the USA) is yoghurt from which the whey has been removed. It's pretty thick and sometimes also referred to as “yoghurt cheese.” In India it's used for example in the dessert Shrikhand, but if a recipe doesn't specify that you should strain the yoghurt, you should assume it's unstrained or briefly strained. Wikipedia says: “In south Asia, regular unstrained yoghurt (dahi), made from cow or water buffalo milk, is often sold in disposable clay pots. Kept for a couple of hours in its clay pot, some of the water evaporates through the clay's pores. But true strained yoghurt (chakka) is made by draining dahi in a cloth.” Should you really only find strained yoghurt, you can probably just thin it back with water or milk.
I should maybe add I don't have first-hand experience with what yoghurt from India tastes like, but I've observed that the ethnic shops in my area and one Indian take-away where I could peer into the kitchen all sell/use the exact same brand of yoghurt, which is an unstrained, set yoghurt with a mild (not too sour) taste.
Basmati is classic. I am particularly fond of brown basmati rice, which has more flavor than white basmati, but it takes longer to cook and will go rancid after 6 months. If basmati is not available, any long-grain rice will suffice; short-grain rice tends to be too sticky.
As for technique, rinse the rice until the rinse-water runs clear. For every cup of rice, use 2 cups of water and 1/2 tsp salt. Bring the water to a boil; add the rice and salt and reduce the heat to a simmer. Cook covered until the liquid has been absorbed and the texture of the rice is tender.
For additions to the rice, you have LOADS of options. You can add a pinch of saffron to the water for a vibrant yellow color and distinctive floral aroma (if you just want color, add 1/2 tsp ground turmeric). You can add chunks of peeled ginger, cracked peppercorns, whole peeled garlic cloves, whole cardamom pods, whole cloves, whole bay leaves, whole kaffir lime leaves, and/or whole stick cinnamon -- amounts and combinations are entirely up to your taste (just remember to remove any bay leaves before serving; remove the others or not as you like, but bay is inedible). You can also add cooked vegetables, such as peas, butter beans, pearl onions, and/or carrots.
Best Answer
In Kerala style cuisine (which is what I'm most familiar with as an eater, not a cook) the rice is a short, white variety that is fried in ghee first. It's very similar to the short grain rice used in Japanese cooking.
I have no idea how this would be packaged in the United States, it's just Rice (for the short grain), or long grain/Basmati rice here. I depend on Indian friends to help me identify the good stuff.
As a cook, I find both the short, white style and plain white basmati work very well. The texture with the short grain rice is smoother, and you can taste more of the milk (or coconut milk) and cardamom. It's also very good served cold. The basmati produces a heartier rice pudding that is enhanced by adding extra raisins and cinnamon. I like this best hot.